Question

In a basebal Champonship series, the victor is the first team to win four games Thus2takes at least four aames and no more than seven games to establih a winner Data on alt peevious Championship series are shown in the accompanying tabile Complete parts (a) through ( m Cick the icon to view the table of previous series lenotht - X Langths of basebal series a. IX denoles the number of games that it takes to complete a senes idenbify the possible vals of the rando vanatle X Relative (Type a whole number Use a comma to separate antwers as needed ) Number of games Frequency Frequency 24 29 b. Do be frst and thed colun of the table provide a proaby dsution tor X7 4 0 200 0242 OA. No. They provide a relative-requency distribution of X, which is not the same as a peobatity disrbution of X 29 0242 0317 OB. Not necessanty They provide a historical tolative-trequency distribution, which may or may nol be he sane as the probatitty distribution of X O C. Yes. They provide a relative-frequency delbubon of X which is the same as a peobatilty distribution of X bécause xis not dscrebe O D. Yes. They provide a relative frequency dstbution, which is the same as a probabilty distiudon tecaue X is a vanable of a Tnde populabon Print Done c. Hstorically, what is the most ikely number of games it takes to complebe a series? d. Historically for a randomly chosen senes, what is the probabilty that it ends in tye games? PIX 5) Round to three decimal places as needed e. Historically, for a randomy chosen series, what is the probabiry that t ends in five or more games? PIX5) (Round to three decimal places as needed) t. The data in the table exhibit a statistcal odsity If the teo eams in a senes are evently matched and one team ahead three games to hwo, either eam has the same chance of winning game number sx Thus there should be about an equal number of so- and seyen-qame series f the teams ane not evenly matched the series should bend o be shorer, ending in sx or fewer gaes nt seven games Choose a plausble explanation of why the series tend to last longer than expected OA. In pame s the team facing eamination may play harder to avoid beng eiminabed OB Ina Champonshp series, the two best teams are often playng Tha means Championship ceries tond to ast longer becane the beams are evenly matched O C. In game si i the teams are almost evenly matched, the sighly beller eam wil lend to underpertom OD. Teams tend to go on winning or losing streaks This means that a team hat wins has a higher chance of wnng the net game ol

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Answer 1

Number of games to win a series in baseball championship, X, frequency,f, and relative frequency, rf X f rf 4 24 0.200 5 29 0.242 6 29 0.242 7 38 0.317 a. Possible values of random variable X is 4,5,6,7. The random variable, X can take any one of the four possible values. b.Option D is correct answer. In finite population, relative frequency is same as the probability. The relative frequency reaches a constant value for 4 games to win, is 0.200 c. Expected value of the the random variable X

3 Ex.rf=5.681 i-0 To complete a series, it takes approximately 6 games on an average in the long run of the series. d. Probability of X=5 Number of obervations of winning 5 games n(A) 29 Total number of games played in a Ef 120 series 29 =0.2417 120 29 -=0.2417 120 Р(X-5)- п(A)

Р(X25) %3P(Х%3D5) +Р(Х-6)+P(Х-7)3D0.242+0.242 +0.317-0.801 е. 29 =0.2417 120 Р(X-6) - п(А) 0.2417+0.2417+0.3167=0.8001 = 38 = 0.3167 120 Р(X-7) - п(А) The probaility that a series ends with 5 or more games is 80.01% f. Option D is correct answer.